Question: Simplify the following expression: $p = \dfrac{-4x^2 + 48x - 80}{x - 10} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-4$ , so we can rewrite the expression: $ p =\dfrac{-4(x^2 - 12x + 20)}{x - 10} $ Then we factor the remaining polynomial: $x^2 {-12}x + {20} $ ${-10} {-2} = {-12}$ ${-10} \times {-2} = {20}$ $ (x {-10}) (x {-2}) $ This gives us a factored expression: $\dfrac{-4(x {-10}) (x {-2})}{x - 10}$ We can divide the numerator and denominator by $(x + 10)$ on condition that $x \neq 10$ Therefore $p = -4(x - 2); x \neq 10$